use the general slicing method to find the volume of the solid. the solid with a semicircular base of radius 18 whose cross sections are perpendicular to the base and parallel to the diameter in squares

Question

use the general slicing method to find the volume of the solid.  the solid with a semicircular base of radius 18 whose cross sections are perpendicular to the base and parallel to the diameter in squares

anonymous · Answer

|dw:1399278661092:dw|
Might look something like this

paki · Answer

In general, the technique of Volumes by Slicing involves slicing up the shape into pieces (called slices), computing the volume of each slice, and then adding them up...  In Calculus, we add things using integration...  So finding volumes by slicing requires that we partition the interval [a,b] into sub-intervals of width dx...  The volume of each slice is then the cross-section area	imes dx...  The result is a general formula is :

paki · Answer

$$\int\limits\limits_{a}^{b} A(x)dx$$

paki · Answer

semi-circular base A(x)=√324−x2... from here find A(x) of squares and put in the formula...  A(x)= 49−x2...

paki · Answer

$$A(x)= \int\limits_{18}^{-18} (324-x^{2}) dx$$

paki · Answer

now solve as per the rules of integration....

anonymous · Answer

why did where the bounds -18 to 18 not 18 to -18?

paki · Answer

look at the figure above... you will know, why i have +18 and -18... its from positive leading to negative...

paki · Answer

and if you want much more, then study this.... it will help you... http://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter31/section05.html